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Nature and our world have a bias! Roughly $30\%$ of the time the number $1$occurs as the leading digit in many datasets base $10$. This phenomenon isknown as Benford's law and it arrises in diverse fields such as the stockmarket, optimizing computers, street addresses, Fibonacci numbers, and is oftenused to detect possible fraud. Based on previous work, we know that differentforms of a one-dimensional stick fragmentation result in pieces whose lengthsfollow Benford's Law. We generalize this result and show that this can beextended to any finite-dimensional ``volume''. We further conjecture that evenlower-dimensional volumes, under the unrestricted fragmentation process, followBenford's Law.

Benford Behavior of a Higher-Dimensional Fragmentation Process